Welch & Peers (1963) used a root-information prior to obtain
posterior probabilities for a scalar parameter exponential model
and showed that these Bayes probabilities had the confidence property
to second order asymptotically. An important undercurrent of this indicates
that the constant information reparameterization provides location
model structure, for which the confidence property was and is well
known. This paper examines the role of the scalar-parameter exponential
model for obtaining approximate probabilities and approximate confidence
levels, and then addresses the extension for the vector-parameter
exponential model.